1. **State the problem:** A zookeeper wants to fence a rectangular habitat for goats. The length $x$ should be at least 80 feet, and the perimeter should be no more than 300 feet. 2. **Write the inequalities:** - Length constraint: $x \geq 80$ - Perimeter constraint: The perimeter $P = 2x + 2y \leq 300$ 3. **Rewrite the perimeter inequality:** $$2x + 2y \leq 300$$ Divide both sides by 2: $$\cancel{2}x + \cancel{2}y \leq \frac{300}{\cancel{2}}$$ $$x + y \leq 150$$ 4. **System of inequalities:** $$\begin{cases} x \geq 80 \\ x + y \leq 150 \end{cases}$$ 5. **Two possible solutions:** - i. $x=80$, $y=50$ (since $80 + 50 = 130 \leq 150$) - ii. $x=90$, $y=40$ (since $90 + 40 = 130 \leq 150$) These satisfy both constraints.